Nonlinear stability of plane rotating shear flow under three—dimensional nondivergence disturbances
Abstract
Nonlinear stability criterion for plane rotating shear flow under threedimensional nondivergence disturbances was obtained by using both variational principle and convexity estimate introduced by Arnold (1965) and Holm et al. (1985). The results obtained in this paper show that the effect of Coriolis force plays an important role in the nonlinear stability criterion, and the nonlinear stability property of the basic flow depends on both the distribution of basic states and the way the external disturbance acts on the states. The upper bound of the gradient of the mass density displacement from the equilibriumk^2 = left { ěe left[ {ρ (bar x,t)ρ _e (bar x)} right]} right^2 /left[ {ρ (bar x,t)ρ _e (bar x)} right]^2 is determined by the basic states and one example was given to show the exact upper value of k. The remarks on Blumen’s paper were also given at Section 4 of this paper.
 Publication:

Advances in Atmospheric Sciences
 Pub Date:
 June 1991
 DOI:
 10.1007/BF02658089
 Bibcode:
 1991AdAtS...8..129R
 Keywords:

 Baroclinic Instability;
 Coriolis Effect;
 Flow Stability;
 Rotating Fluids;
 Shear Flow;
 Three Dimensional Flow;
 Computational Fluid Dynamics;
 Nonlinear Equations;
 Variational Principles;
 Fluid Mechanics and Heat Transfer